Iterative Learning Control Using Adjoint Systems and Stable Inversion

ABSTRACTIn this paper, we investigate iterative learning control (ILC) for non‐minimum phase systems from a novel viewpoint. For non‐minimum phase systems, the magnitude of a desiredinput obtained by ILC using forward‐time updating and Silverman's inversion are too large because of the influence of the unstable zeros. On the other hand, stable inversion constructs a bounded desired input by using non‐causal inverse for non‐minimum phase systems.In this paper, we first clarify that ILC using an adjoint system achieves the desired input defined by stable inversion. Hence, ILC using an adjoint system is an effective method for the control of non‐minimum phase systems with uncertainty. However, a useful convergence condition of ILC using an adjoint system was not achieved. Next, we develop a simple convergence condition in the frequency domain.